{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:20Z","timestamp":1747198040287,"version":"3.40.5"},"reference-count":34,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["G0F6718N"],"award-info":[{"award-number":["G0F6718N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The problem is considered of approximately solving a system of univariate polynomials with one or more common roots and its coefficients corrupted by noise. The goal is to estimate the underlying common roots from the noisy system. Symbolic algebra methods are not suitable for this. New Rayleigh quotient methods are proposed and evaluated for estimating the common roots. Using tensor algebra, reasonable starting values for the Rayleigh quotient methods can be computed. The new methods are compared to Gauss\u2013Newton, solving an eigenvalue problem obtained from the generalized Sylvester matrix, and finding a cluster among the roots of all polynomials. In a simulation study it is shown that Gauss\u2013Newton and a new Rayleigh quotient method perform best, where the latter is more accurate when other roots than the true common roots are close together.<\/jats:p>","DOI":"10.1515\/cmam-2018-0025","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T11:09:48Z","timestamp":1531393788000},"page":"147-163","source":"Crossref","is-referenced-by-count":1,"title":["Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials"],"prefix":"10.1515","volume":"19","author":[{"given":"Alwin","family":"Stegeman","sequence":"first","affiliation":[{"name":"Group Science, Engineering and Technology , KU Leuven \u2013 Kulak, E. Sabbelaan 53, 8500 Kortrijk ; and Department of Electrical Engineering (ESAT), KU Leuven, Kasteelpark Arenberg 10, 3001 Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5562-5014","authenticated-orcid":false,"given":"Lieven","family":"De Lathauwer","sequence":"additional","affiliation":[{"name":"Group Science, Engineering and Technology , KU Leuven \u2013 Kulak, E. Sabbelaan 53, 8500 Kortrijk ; and Department of Electrical Engineering (ESAT), KU Leuven, Kasteelpark Arenberg 10, 3001 Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,7,12]]},"reference":[{"key":"2023033110133750792_j_cmam-2018-0025_ref_001_w2aab3b7e1333b1b6b1ab2ab1Aa","unstructured":"S.  Barnett,\nPolynomials and Linear Control Systems,\nMonogr. Textb. Pure Appl. 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